The big right-arm fast bowler left the field midway through his second over in the final session on day two of the Test and didn’t return.
Hazlewood had been running into bowl but slowed down, appearing to suffer a leg injury as he accelerated.
Cricket Australia later confirmed that Hazlewood had sustained a left hamstring injury and been sent for an MRI scan.
The injury was the only setback for Australia on a dominant second day where they bowled out for 416, before taking five final session wickets to have the Black Caps 5-109 in reply.
Hazlewood did claim one scalp before his injury, bowling Jeet Raval for 1, but it was Mitchell Starc who took four wickets.
Steve Smith produced a sensational one-handed diving catch at second slip to dismiss Kane Williamson for 34.
Ross Taylor led the resistance and will resume on day three on 66, alongside BJ Watling on 0.
New Zealand bowled for two sessions earlier in the day without debutant Ferguson who sustained a calf injury on day one.
The Black Caps confirmed that Ferguson had a right calf muscle tendon strain and wouldn’t bowl again in the match, but would bat.
Both injuries put doubts on both players given the tight schedule of the series, with the Second Test on Boxing Day at the MCG.
New Zealand are optimistic they’ll have left-arm paceman Trent Boult available in Melbourne, while James Pattinson and 12th man Michael Neser will come into contention for Australia if Hazlewood is ruled out.